%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ITP209_1 : TPTP v9.2.0. Released v8.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:51:27 PM UTC 2025 % Result : Theorem 4.16s 4.33s % Output : Proof 4.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : ITP209_1 : TPTP v9.2.0. Released v8.0.0. % 0.07/0.15 % Command : duper %s % 0.14/0.36 % Computer : n006.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Oct 2 23:35:08 EDT 2025 % 0.14/0.36 % CPUTime : % 4.16/4.33 SZS status Theorem for theBenchmark.p % 4.16/4.33 SZS output start Proof for theBenchmark.p % 4.16/4.33 Clause #1 (by assumption #[]): Eq (∀ (A B : a), Eq (aa_a_a (aa_a_fun_a_a f A) B) (aa_a_a (aa_a_fun_a_a f B) A)) True % 4.16/4.33 Clause #2 (by assumption #[]): Eq % 4.16/4.33 (∀ (A B C : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f A) (aa_a_a (aa_a_fun_a_a f B) C)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f B) (aa_a_a (aa_a_fun_a_a f A) C))) % 4.16/4.33 True % 4.16/4.33 Clause #12 (by assumption #[]): Eq % 4.16/4.33 (Not % 4.16/4.33 (Eq (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) b)) c) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) c)) b))) % 4.16/4.33 True % 4.16/4.33 Clause #29 (by clausification #[1]): ∀ (a_1 : a), Eq (∀ (B : a), Eq (aa_a_a (aa_a_fun_a_a f a_1) B) (aa_a_a (aa_a_fun_a_a f B) a_1)) True % 4.16/4.33 Clause #30 (by clausification #[29]): ∀ (a_1 a_2 : a), Eq (Eq (aa_a_a (aa_a_fun_a_a f a_1) a_2) (aa_a_a (aa_a_fun_a_a f a_2) a_1)) True % 4.16/4.33 Clause #31 (by clausification #[30]): ∀ (a_1 a_2 : a), Eq (aa_a_a (aa_a_fun_a_a f a_1) a_2) (aa_a_a (aa_a_fun_a_a f a_2) a_1) % 4.16/4.33 Clause #33 (by clausification #[2]): ∀ (a_1 : a), % 4.16/4.33 Eq % 4.16/4.33 (∀ (B C : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f B) C)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f B) (aa_a_a (aa_a_fun_a_a f a_1) C))) % 4.16/4.33 True % 4.16/4.33 Clause #34 (by clausification #[33]): ∀ (a_1 a_2 : a), % 4.16/4.33 Eq % 4.16/4.33 (∀ (C : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f a_2) C)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_2) (aa_a_a (aa_a_fun_a_a f a_1) C))) % 4.16/4.33 True % 4.16/4.33 Clause #35 (by clausification #[34]): ∀ (a_1 a_2 a_3 : a), % 4.16/4.33 Eq % 4.16/4.33 (Eq (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f a_2) a_3)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_2) (aa_a_a (aa_a_fun_a_a f a_1) a_3))) % 4.16/4.33 True % 4.16/4.33 Clause #36 (by clausification #[35]): ∀ (a_1 a_2 a_3 : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f a_2) a_3)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_2) (aa_a_a (aa_a_fun_a_a f a_1) a_3)) % 4.16/4.33 Clause #38 (by superposition #[36, 31]): ∀ (a_1 a_2 a_3 : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a_1) a_2)) a_3) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f a_3) a_2)) % 4.16/4.33 Clause #54 (by superposition #[38, 31]): ∀ (a_1 a_2 a_3 : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a_1) a_2)) a_3) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_2) (aa_a_a (aa_a_fun_a_a f a_3) a_1)) % 4.16/4.33 Clause #59 (by superposition #[54, 38]): ∀ (a_1 a_2 a_3 : a), % 4.16/4.33 Eq (aa_a_a (aa_a_fun_a_a f a_1) (aa_a_a (aa_a_fun_a_a f a_2) a_3)) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f a_3) (aa_a_a (aa_a_fun_a_a f a_2) a_1)) % 4.16/4.33 Clause #129 (by clausification #[12]): Eq % 4.16/4.33 (Eq (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) b)) c) % 4.16/4.33 (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) c)) b)) % 4.16/4.33 False % 4.16/4.33 Clause #130 (by clausification #[129]): Ne (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) b)) c) (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) c)) b) % 4.16/4.33 Clause #131 (by forward demodulation #[130, 31]): Ne (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f a2) b)) (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) c)) b) % 4.16/4.33 Clause #132 (by forward demodulation #[131, 31]): Ne (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f b) a2)) (aa_a_a (aa_a_fun_a_a f (aa_a_a (aa_a_fun_a_a f a2) c)) b) % 4.16/4.33 Clause #133 (by forward demodulation #[132, 31]): Ne (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f b) a2)) (aa_a_a (aa_a_fun_a_a f b) (aa_a_a (aa_a_fun_a_a f a2) c)) % 4.16/4.33 Clause #134 (by forward demodulation #[133, 59]): Ne (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f b) a2)) (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f a2) b)) % 4.16/4.33 Clause #135 (by forward demodulation #[134, 31]): Ne (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f b) a2)) (aa_a_a (aa_a_fun_a_a f c) (aa_a_a (aa_a_fun_a_a f b) a2)) % 4.16/4.33 Clause #136 (by eliminate resolved literals #[135]): False % 4.16/4.33 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------